## Question

###### Continuous random variables Xand have a joint probability density functionf(x)-2.0-1.2x-0.8yfor (x) in the first quadrant unit square [0,1]x[0,1] show that flxv) is a legitimate probability density function on the unit square b) find the marginal densities fx(x) and fyly) compute E[X] and var(X) set up only (you needn't evaluate) integral expressions for the following probabilities P(X+Y>1) (sketch the region in the unit square) P(Y<X) (sketch the region in the unit square P(X<0.25

Continuous random variables Xand have a joint probability density function f(x)-2.0-1.2x-0.8y for (x) in the first quadrant unit square [0,1]x[0,1] show that flxv) is a legitimate probability density function on the unit square b) find the marginal densities fx(x) and fyly) compute E[X] and var(X) set up only (you needn't evaluate) integral expressions for the following probabilities P(X+Y>1) (sketch the region in the unit square) P(Y<X) (sketch the region in the unit square P(X<0.25 Y<0.25) (sketch the "numerator" in the unit square)

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